CN112947063A - Non-fragile fuzzy proportional integral control method of attenuation channel networking system - Google Patents
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Abstract
The invention discloses a non-fragile fuzzy proportional-integral control method of an attenuation channel networking system, and mainly relates to the field of control. Establishing a system state space model based on a Takagi-Sugeno fuzzy technology; establishing a transmission model under the influence of channel attenuation; constructing a fuzzy proportional-integral controller based on the available measurement output; constructing a performance index auxiliary function, and obtaining a value of the gain of the controller by solving a proposed optimization algorithm according to the auxiliary function; and finally, calculating to obtain a control signal based on the obtained controller gain. The invention has the beneficial effects that: the method combines two technologies of fuzzy control and proportional-integral control, has good control effect, and ensures the easy execution of the algorithm because the key variables adopt a method for solving the linear matrix inequality.
Description
Technical Field
The invention relates to the field of control, in particular to a non-fragile fuzzy proportional-integral control method of an attenuation channel networking system.
Background
Dissipation control is one of basic research problems of control theory and has important significance in practical engineering. The basic idea of dissipation control is to use a measurable signal and adopt a proper control algorithm to enable a controlled system to meet a specified dissipation performance index under the action of the control algorithm. Dissipation control theory provides a unified framework to study H∞Classical performance indexes such as control and passive control. In order to meet different industrial requirements since the last decades, many control algorithms have been proposed to achieve dissipation control and to achieve satisfactory results in practice.
Nonlinear systems widely exist in reality, and compared with linear systems, the nonlinear systems do not meet the superposition theorem and have more complex dynamic behaviors, so that the design of a control algorithm for the nonlinear systems is always a hot point problem. Among the many control algorithms for non-linear systems, fuzzy control is generally considered to be a very effective algorithm. Under the fuzzy control framework, an original nonlinear system is firstly expressed into a fuzzy system, and then a corresponding fuzzy control algorithm is designed according to human knowledge, experience and fuzzy theory, and the algorithm has clear physical meaning and is easy to implement. Commonly used fuzzy control algorithms include fuzzy proportional control and fuzzy proportional-integral control. In the fuzzy proportional-integral control algorithm, an integral term is introduced, so that the algorithm is insensitive to noise and can eliminate steady-state errors, and therefore the fuzzy proportional-integral control algorithm is more commonly used in practical engineering. On the other hand, when the control algorithm is implemented in practice, due to factors such as aging of controller elements and calculation errors, control parameters in the designed control algorithm are prone to perturbation, and therefore the effectiveness of the algorithm is affected, and therefore the design of a non-fragile control algorithm has important practical significance. Under a non-fragile control framework, the controlled system may be somewhat robust to control parameter perturbations.
In modern industrial production, information transfer in the system is usually accomplished by a communication network. The use of a communication network reduces flex cables, reduces costs, and increases transmission flexibility. However, in practice, the bandwidth of the communication network is limited, and when a large amount of data is transmitted in the network at the same time, data congestion is easily caused, and then some adverse effects are caused, such as transmission skew, channel attenuation, and the like. Among them, channel fading is the most common network-induced phenomenon, which greatly affects the performance of the controlled system if not properly considered in designing the control algorithm.
Based on the above situation, in order to meet the requirements of practical industrial application, a non-fragile fuzzy proportional-integral technology-based dissipation control method for solving the nonlinear system under the influence of channel attenuation is urgently needed, that is, a non-fragile fuzzy proportional-integral dissipation control method is developed for a networked nonlinear system containing an attenuation channel, and is used for controlling the system in real time and ensuring the safe operation of the system.
Disclosure of Invention
The invention aims to provide a non-fragile fuzzy proportional integral control method of an attenuation channel networking system, which
In order to achieve the purpose, the invention is realized by the following technical scheme:
a non-fragile fuzzy proportional integral control method for fading channel networked system, comprising the steps of:
s1, establishing a system state space model based on a Takagi-Sugeno fuzzy modeling technology,
s2, establishing a signal transmission model under the influence of channel attenuation to realize data transmission between the nonlinear system and the controller;
s3, constructing proportional gains corresponding to the fuzzy mode j and the estimation mode n of the controller based on the available measurement outputIntegral gains corresponding to controller fuzzy mode j and estimation mode nObtaining the value of the gain of the controller according to an auxiliary function, a Lyapunov stability theory and a convex optimization technology; wherein j is 1, 2, …,r,
S4, according to the obtained proportional gain of the controllerAnd integral gainThe control signal is calculated and the control signal is calculated,
from the state space model of the system in step S1, the signal transmission model in step S2, and the controller gain in step S3, the following fuzzy proportional-integral controller is constructed:
wherein,a proportional term representing the amount of the controller,the integral term representing the controller, and the control signal to be applied to the controlled object can be calculated according to equation (7).
Further, the method for establishing a system state space model of step S1 includes using the following formula:
x (k) represents the state variable of the nonlinear system at time k, and x (k) is nxA dimension column vector;
y (k) represents the measured output signal of the nonlinear system at time k, y (k) being nyA dimension column vector;
z (k) represents the signal to be controlled at time k, and z (k) is nzA dimension column vector;
u (k) represents the control signal of the nonlinear system at time k, u (k) is nuA dimension column vector;
w (k) represents energy-bounded noise, w (k) being nwA dimension column vector; n isx、ny、nu、nz、nwIs a known positive integer;
r represents the total number of fuzzy rules, and r is a known positive integer;
ρ (k) represents a vector consisting of detectable states or measurement outputs; phi is ai(rho (k)) is a membership function of the fuzzy system and represents the weight of the ith fuzzy mode in the whole nonlinear system at the moment k;
Airepresenting the system matrix, C the output matrix, BiRepresenting an input matrix, EiRepresenting process noise matrix, F representing measurement noise matrix, GiRepresenting a signal matrix to be controlled; wherein A isi、C、Bi、Ei、F、GiThe matrices are all known constant matrices.
Further, the establishing a signal transmission model under the influence of channel attenuation in step S2, and implementing data transmission between the nonlinear system and the controller includes:
assuming channel sharingIn a single mode, in combinationIndicating the modality the channel is in at time k,represents a known positive integer;
σ (k) represents a discrete-time Markov random process with a state transition matrix Wherein matrix element 0 ≦ πabThe scalar quantity with 1 ≦ known represents the probability of a transition from modality a to modality b, i.e.Wherein Pr {. cndot.) represents the probability of occurrence of the event ". cndot.",representing a definition symbol;
according to the output equation in the system model established in S1, under the influence of channel attenuation, the transmitted signal can be expressed as:
wherein,represents the measured output after being affected by the channel attenuation, i.e. the signal actually received by the controller;
reflecting the channel fading phenomenon, diag { … } represents the diagonal block matrix, χc,σ(k)(k) Represents a random process of mean valueCovariance of Is a known scalar quantity, and
a modality estimator is employed to estimate the modality of the network, σ (k). Suppose that the mode estimated by the mode estimator is theta (k) with a value range of theta (k) Is a known positive integer with detection probabilityδefIs a known scalar quantity, satisfies
Further, the auxiliary function is constructed, and the proportional gain of the controller is calculatedAnd integral gainConstructing the following auxiliary functions according to the system state space model in the step S1 and the signal transmission model in the step S2:
wherein V (k, σ (k)) represents a selected Lyapunov function, J (S)1,S2,S3K) represents the auxiliary function introduced for the dissipative performance indicator, κ ∈ {0, 1} is a given scalar,and S2Is a known matrix, Pσ(k)Is a matrix variable to be solved;
eta (k) is a variable after the system state and the controller integral term are subjected to dimension increase;
formula (3) is used for analyzing the stability of the system (1), and formula (4) is used for analyzing the dissipative property of the system (1);
according to the auxiliary function, the Lyapunov stability theory and the convex optimization technology, the following steps are executed to obtain the gain of the controller:
s31, solving the following linear matrix inequalities (5) - (7) to obtain a set of initial solutions Pt,Xt,Rijtn,λ1,λ2,αijtn:
"+" represents the symmetric part of the symmetric matrix, I represents the unit matrix with proper dimension, 0 in the left matrix with unequal number represents the zero matrix block with proper dimension;
whereinj=1,2,…,r,Perturbation correlation matrix for parameters in proportional gain of the controller;
wherein N isIPerturbing a correlation matrix for parameters in the integral gain of the controller;wherein,
let Pt(0)=Pt,Xt(0)=Xt,Rijtn(0)=Rijtn,λ1(0)=λ1,λ2(0)=λ2,αijtn(0)=αijtn,Wherein the variable with subscript (0) represents the algorithm initial value;
s32, solving an optimization problem under the constraints of the formulas (5) to (7):wherein, min represents the minimum function, tr represents the trace of matrix;
s33, using the matrix X in the two inequalities in the formula (5)tBy substitution of PtThe newly obtained inequalities are respectively marked as H1<0,H2< 0, and the matrix P obtained in step S32t,Rijtn,λ1,λ2,αijtnInto formula H1<0,H2< 0 and equation (6), if these equations are all true and satisfy:
where v > 0 is a given scalar representing the accuracy of the algorithm;
| a | represents solving the absolute value of a;
s34, ifIf the step length is larger than the given step length, quitting; otherwise, it orders Return to execution S32;
the proportional gain of the controller can be obtained through the above steps S31-S34And integral gain
Compared with the prior art, the invention has the beneficial effects that:
as mentioned above, the invention provides a non-fragile fuzzy proportional-integral control method of a non-linear system under the influence of channel attenuation, which simultaneously considers the common channel attenuation phenomenon and controller parameter perturbation phenomenon in networked communication and combines two technologies of fuzzy control and proportional-integral control to construct a non-fragile fuzzy proportional-integral controller, and the controller can effectively solve the non-fragile control problem of the non-linear system under the influence of channel attenuation and has good control effect. In addition, the convex optimization method is adopted in the solving process of the key variable (controller gain), so that the method is easy to execute.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 shows a trace of a measurement signal y (k) and its signal after being affected by channel attenuationThe solid line in the graph is the trace of the measurement signal y (k), and the double-dashed line is the attenuation signalA trajectory;
FIG. 3 is open loop system state x1(k) And x2(k) Trace diagram, in which the solid line is the first component x of the open-loop system state1(k) Trace, double-dashed line for second component x of open-loop system state2(k) A trajectory;
FIG. 4 is a closed loop system state x1(k) And x2(k) Trace diagram, in which the solid line is the first component x of the open-loop system state1(k) Trace, double-dashed line for second component x of open-loop system state2(k) A trajectory;
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and these equivalents also fall within the scope of the present application.
The embodiment describes a fuzzy proportional-integral non-fragile control method of a non-linear system under the influence of channel attenuation, which is based on a fuzzy proportional-integral technology to solve a class of non-fragile control problems of the non-linear system under the influence of the channel attenuation.
As shown in fig. 1, a fuzzy proportional-integral state estimation method for a nonlinear system under the influence of channel attenuation includes the following steps:
s1, establishing a system state space model based on a Takagi-Sugeno fuzzy modeling technology, as shown in a formula (1):
wherein x (k) represents the state variable of the nonlinear system at the time k, and x (k) is nxA dimension column vector;
u (k) represents the measured output signal of the nonlinear system at time k, y (k) is nyA dimension column vector;
z (k) represents the signal to be controlled at time k, and z (k) is nzA dimension column vector;
u (k) represents the control signal of the nonlinear system at time k, u (k) is nuA dimension column vector;
w (k) represents energy-bounded noise, w (k) being nwA dimension column vector; n isx、ny、nu、nz、nwIs a known positive integer;
e represents the total number of fuzzy rules, and r is a known positive integer;
ρ (k) represents a vector consisting of detectable states or measurement outputs; phi is ai(rho (k)) is a membership function of the fuzzy system and represents the weight of the ith fuzzy mode in the whole nonlinear system at the moment k;
Airepresenting the system matrix, C the output matrix, BiRepresenting an input matrix, EiRepresenting process noise matrix, F representing measurement noise matrix, GiRepresenting a signal matrix to be controlled; wherein A isi、C、Bi、Ei、F、GiThe matrixes are all known constant matrixes;
s2, establishing a signal transmission model under the influence of channel attenuation to realize data transmission between the nonlinear system and the controller;
without loss of generality, it is assumed that the channels are commonIn a single mode, in combinationIndicating the modality the channel is in at time k,represents a known positive integer;
σ (k) represents a discrete-time Markov random process with a state transition matrixWherein matrix element 0 ≦ πabThe scalar quantity with 1 ≦ known represents the probability of a transition from modality a to modality b, i.e.Wherein Pr {. cndot.) represents the probability of occurrence of the event ". cndot.",representing a definition symbol;
according to the output equation in the system model established in S1, under the influence of channel attenuation, the transmitted signal can be expressed as:
wherein,represents the measured output after being affected by the channel attenuation, i.e. the signal actually received by the controller;
reflecting the channel fading phenomenon, diag { … } represents a diagonal block matrix,χc,σ(k)(k) Represents a random process of mean valueCovariance of Is a known scalar quantity, and
in engineering practice, it is difficult to obtain the real mode of the network in real time due to factors such as complex environment, and therefore a mode estimator is often used to estimate the mode σ (k) of the network. Suppose that the mode estimated by the mode estimator is theta (k) with a value range of theta (k) Is a known positive integer with detection probabilityδefIs a known scalar quantity, satisfies
S3, constructing an auxiliary function and calculating the proportional gain of the controllerAnd integral gain
Wherein,representing proportional gains corresponding to the controller fuzzy mode j and the estimation mode n;the integral gain corresponding to the controller fuzzy mode j and the estimation mode n is shown, j is 1, 2, …, r,
specifically, the following auxiliary functions are constructed according to the system state space model in step S1 and the signal transmission model in step S2:
wherein V (k, σ (k)) represents a selected Lyapunov function, J (S)1,S2,S3K) represents the helper function introduced for the dissipative performance indicator, k e 1, 1 is a given scalar,and S2Is a known matrix, Pσ(k)Is a matrix variable to be solved;
eta (k) is a variable after the system state and the controller integral term are subjected to dimension increase;
formula (3) is used for analyzing the stability of the system (1), and formula (4) is used for analyzing the dissipative property of the system (1);
according to the auxiliary function, the Lyapunov stability theory and the convex optimization technology, the following steps are executed to obtain the gain of the controller:
s31, solving the following linear matrix inequalities (5) - (7) to obtain a set of initial solutions Pt,Xt,Rijtn,λ1,λ2,αijtn:
"+" represents the symmetric part of the symmetric matrix, I represents the unit matrix with proper dimension, 0 in the left matrix with unequal number represents the zero matrix block with proper dimension;
s32, solving an optimization problem under the constraints of the formulas (5) to (7):wherein, min represents the minimum function, tr represents the trace of matrix;
s33, using the matrix X in the two inequalities in the formula (5)tBy substitution of PtThe newly obtained inequalities are respectively marked as H1<0,H2< 0, and the matrix P obtained in step S32t,Rijtn,λ1,λ2,αijtnInto formula H1<0,H2< 0 and equation (6), if these equations are all true and satisfy:
wherein upsilon > 0 is a given scalar and represents the precision of the algorithm;
| a | represents solving the absolute value of a;
s34, ifIf the step length is larger than the given step length, quitting; otherwise, it orders Return to execution S32;
the proportional gain of the controller can be obtained through the above steps S31-S34And integral gain
S4, according to the obtained proportional gain of the controllerAnd integral gainCalculating a control signal:
from the state space model of the system in step S1, the signal transmission model in step S2, and the controller gain in step S3, taking into account the influence of the perturbation of the controller parameters and the channel attenuation, the following fuzzy proportional-integral controller is constructed, as shown in equation (7):
wherein,a proportional term representing the amount of the controller,the integral term representing the controller, and the control signal to be applied to the controlled object can be calculated according to equation (7).
As can be seen from the formula (7), the fuzzy proportional-integral controller designed by the invention fully considers the influence of channel attenuation, is applied to the mode estimated by the mode estimator, and is more beneficial to practical application while improving the design freedom. On the other hand, the control algorithm of the invention can meet the requirements due to the fact that the perturbation of the controller parameters is fully considered in the design process of the control algorithmUnder the influence of the perturbation of the controller parameters, good control effect can still be provided, whereinA parameter perturbation indicating a possible occurrence of the proportional gain of the controller,indicating the integral gain parameter perturbation that may occur to the controller,NP,NIin the form of a known matrix, which is,representing an unknown time-varying matrix and I an identity matrix. Thus, the non-fragile controller designed has good robustnessAnd (4) the bar property.
In addition, compared with the existing method in the prior art, the method has the following advantages:
compared with the traditional fuzzy proportional control method, the control method has the advantages that the integral link is introduced, so that the steady-state error can be eliminated, the robustness of the controller is improved, and the control method is better.
Compared with the traditional mode-dependent control method, the method provided by the invention has wider applicability because the network mode is difficult to obtain in real time and the controller is designed only by utilizing the estimated mode in consideration of the fact that the network mode is difficult to obtain in real time.
The method is used for controlling the industrial system in real time and can better meet the application requirements of the actual industry.
The fuzzy proportional-integral non-fragile control method of the nonlinear system under the influence of the channel attenuation provided by the invention is explained by combining experiments to verify the effectiveness of the method provided by the invention.
In the experiment process, the experiment step length is taken as 100, channel attenuation and controller perturbation parameters are added on a semi-physical simulation platform in a simulated mode, and the output given by the platform and subjected to channel attenuation is transmitted to a computer to serve as the input of a non-fragile fuzzy proportional-integral controller.
The method provided by the invention is utilized to generate a control signal, and the control signal is transmitted to a semi-physical simulation platform system to control the system. In this experiment, the system state is a 2-dimensional column vector, and the measurement output is a 1-dimensional scalar.
First, values of the system measurement output and the output after being affected by the channel attenuation are obtained by a computer, and a drawing tool of Matlab software of the computer is used to obtain the graph 2. As can be seen from fig. 2:
the system measurement output has obvious attenuation on the amplitude under the influence of channel attenuation, and the influence of the channel attenuation on the system performance is indirectly reflected.
In a similar way, the first component x of the state of the open-loop system (without control action) is taken from the computer1(k) And a second component x2(k) Using computer Matlab softwareThe drawing tool obtains fig. 3. As can be seen from fig. 3:
both components of the open loop system state are divergent, i.e., the open loop system is unstable.
In a similar way, the first component x of the state of the closed-loop system (adding control action) is calculated by computer1(k) And a second component x2(k) And obtaining the graph 4 by utilizing a drawing tool of Matlab software of a computer. As can be seen from fig. 4:
by using the control algorithm proposed by the invention, both components of the closed-loop system state can quickly reach the equilibrium point (origin of coordinates) despite the channel attenuation and the perturbation of the controller parameters, i.e. the closed-loop system is stable, and the effectiveness of the invention is reflected.
Claims (4)
1. A non-fragile fuzzy proportional integral control method for fading channel networking system, comprising the steps of:
s1, establishing a system state space model based on a Takagi-Sugeno fuzzy modeling technology,
s2, establishing a signal transmission model under the influence of channel attenuation to realize data transmission between the nonlinear system and the controller;
s3, constructing proportional gains corresponding to the fuzzy mode j and the estimation mode n of the controller based on the available measurement outputIntegral gains corresponding to controller fuzzy mode j and estimation mode nObtaining the value of the gain of the controller according to an auxiliary function, a Lyapunov stability theory and a convex optimization technology; where j is 1, 2, …, r,
s4, according to the obtained proportional gain of the controllerAnd integral gainThe control signal is calculated and the control signal is calculated,
from the state space model of the system in step S1, the signal transmission model in step S2, and the controller gain in step S3, the following fuzzy proportional-integral controller is constructed:
2. The method of claim 1, wherein the step S1 of establishing a system state space model comprises using the following formula:
x (k) represents the state variable of the nonlinear system at time k, and x (k) is nxA dimension column vector;
y (k) represents the measured output signal of the nonlinear system at time k, y (k) being nyA dimension column vector;
z (k) represents the signal to be controlled at time k, and z (k) is nzA dimension column vector;
u (k) denotes the time kControl signal for non-linear system, u (k) being nuA dimension column vector;
ω (k) represents energy-bounded noise, ω (k) being nωA dimension column vector; n isx、ny、nu、nz、nωIs a known positive integer;
r represents the total number of fuzzy rules, and r is a known positive integer;
ρ (k) represents a vector consisting of detectable states or measurement outputs; phi is ai(rho (k)) is a membership function of the fuzzy system and represents the weight of the ith fuzzy mode in the whole nonlinear system at the moment k;
Airepresenting the system matrix, C the output matrix, BiRepresenting an input matrix, EiRepresenting process noise matrix, F representing measurement noise matrix, GiRepresenting a signal matrix to be controlled; wherein A isi、C、Bi、Ei、F、GiThe matrices are all known constant matrices.
3. The method as claimed in claim 1, wherein the step S2 of establishing a signal transmission model under the influence of channel attenuation for implementing data transmission between the nonlinear system and the controller comprises:
assuming channel sharingIn a single mode, in combinationIndicating the modality the channel is in at time k,represents a known positive integer;
σ (k) represents a discrete-time Markov random process with a state transition matrixWherein matrix element 0 ≦ πabThe scalar quantity with 1 ≦ known represents the probability of a transition from modality a to modality b, i.e.Wherein Pr {. cndot.) represents the probability of occurrence of the event ". cndot.",representing a definition symbol;
according to the output equation in the system model established in S1, under the influence of channel attenuation, the transmitted signal can be expressed as:
wherein,represents the measured output after being affected by the channel attenuation, i.e. the signal actually received by the controller;
reflecting the channel fading phenomenon, diag { … } represents the diagonal block matrix, χc,σ(k)(k) Representing a sequence of random variables having a mean value ofCovariance of Is a known scalar quantity, and
4. The method as claimed in claims 2 and 3, wherein the constructing of the auxiliary function calculates the proportional gain of the controllerAnd integral gainConstructing the following auxiliary functions according to the system state space model in the step S1 and the signal transmission model in the step S2:
wherein, V (k, sigma (k)) is shown in the tableSelection of Lyapunov function, J (S)1,S2,S3K) represents the auxiliary function introduced for the dissipative performance indicator, κ ∈ {0, 1} is a given scalar,and S2Is a known matrix, Pσ(k)Is a matrix variable to be solved;
eta (k) is a variable after the system state and the controller integral term are subjected to dimension increase;
formula (3) is used for analyzing the stability of the system (1), and formula (4) is used for analyzing the dissipative property of the system (1);
according to the auxiliary function, the Lyapunov stability theory and the convex optimization technology, the following steps are executed to obtain the gain of the controller:
s31, solving the following linear matrix inequalities (5) - (7) to obtain a set of initial solutions Pt,Xt,Rijtn,λ1,λ2,αijtn:
"+" represents the symmetric part of the symmetric matrix, I represents the unit matrix with proper dimension, 0 in the left matrix with unequal number represents the zero matrix block with proper dimension;
πti,Is an element in the state probability transition matrix, the definition of which is given in S2;
wherein N isIPerturbing a correlation matrix for parameters in the integral gain of the controller;wherein,
let Pt(0)=Pt,Xt(0)=Xt,Rijtn(0)=Rijtn,λ1(0)=λ1,λ2(0)=λ2,αijtn(0)=αijtnAnd iota is 0, wherein the variable with the subscript (0) representsAn algorithm initial value;
s32, solving an optimization problem under the constraints of the formulas (5) to (7):wherein, min represents the minimum function, tr represents the trace of matrix;
s33, using the matrix X in the two inequalities in the formula (5)tBy substitution of PtThe newly obtained inequalities are respectively marked as H1<0,H2< 0, and the matrix P obtained in step S32t,Rijtn,λ1,λ2,αijtnInto formula H1<0,H2< 0 and equation (6), if these equations are all true and satisfy:
wherein upsilon > 0 is a given scalar and represents the precision of the algorithm;
| a | represents solving the absolute value of a;
s34, if the iota is larger than the given step length, exiting; otherwise, let iota +1, Pt(ι)=Pt,Xt(ι)=Xt,Rijtn(ι)=Rijtn,λ1(ι)=λ1,λ2(ι)=λ2,αijtn(ι)=αijtnReturning to execution S32;
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